All green wants to open a franchise in a new neighborhood and wants to estimate
ID: 2932134 • Letter: A
Question
All green wants to open a franchise in a new neighborhood and wants to estimate its potential sales. The store will have 3000 square feet; will serve 10,000 households; will invest $8,000 in advertising; will have 4 competitors in the area; and will carry $45,500 in inventories
For the following problem provide:
–Correlation analysis
–Regression analysis
Explain your decision making and interpret your results.
Annual sales [$000]
Area
Inventory [$000]
Advertising [$000]
Households[000]
Competitors
[1000 sft]
231
3
29.4
8.2
8.2
11
156
2.2
23.2
6.9
4.1
12
10
0.5
14.9
3
4.3
15
519
5.5
60
12
16.1
1
437
4.4
56.7
10.6
14.1
5
487
4.8
57.1
11.8
12.7
4
299
3.1
51.2
8.1
10.1
10
195
2.5
34.7
7.7
8.4
12
20
1.2
21.2
3.3
2.1
15
68
0.6
10.2
4.9
4.7
8
570
5.4
78.8
17.4
12.3
1
428
4.2
57.7
10.5
14
7
464
4.7
53.5
11.3
15
3
15
0.6
16.3
2.5
2.5
14
65
1.2
16.8
4.7
3.3
11
98
1.6
15.1
4.6
2.7
10
398
4.3
34.2
5.5
16
4
161
2.6
19.6
7.2
6.3
13
397
3.8
45.3
10.4
13.9
7
497
5.3
51.8
11.5
16.3
1
528
5.6
61.5
12.3
16
0
99
0.8
27.8
2.8
6.5
14
0.5
1.1
14.2
3.1
1.6
12
347
3.6
46.1
9.6
11.3
6
341
3.5
38.2
9.8
11.5
5
507
5.1
59
12
15.7
0
400
8.6
51.7
7
12
8
Annual sales [$000]
Area
Inventory [$000]
Advertising [$000]
Households[000]
Competitors
[1000 sft]
231
3
29.4
8.2
8.2
11
156
2.2
23.2
6.9
4.1
12
10
0.5
14.9
3
4.3
15
519
5.5
60
12
16.1
1
437
4.4
56.7
10.6
14.1
5
487
4.8
57.1
11.8
12.7
4
299
3.1
51.2
8.1
10.1
10
195
2.5
34.7
7.7
8.4
12
20
1.2
21.2
3.3
2.1
15
68
0.6
10.2
4.9
4.7
8
570
5.4
78.8
17.4
12.3
1
428
4.2
57.7
10.5
14
7
464
4.7
53.5
11.3
15
3
15
0.6
16.3
2.5
2.5
14
65
1.2
16.8
4.7
3.3
11
98
1.6
15.1
4.6
2.7
10
398
4.3
34.2
5.5
16
4
161
2.6
19.6
7.2
6.3
13
397
3.8
45.3
10.4
13.9
7
497
5.3
51.8
11.5
16.3
1
528
5.6
61.5
12.3
16
0
99
0.8
27.8
2.8
6.5
14
0.5
1.1
14.2
3.1
1.6
12
347
3.6
46.1
9.6
11.3
6
341
3.5
38.2
9.8
11.5
5
507
5.1
59
12
15.7
0
400
8.6
51.7
7
12
8
Explanation / Answer
Solution:
For the given data, first of all we have to find out the correlation coefficients exists between the different pairs of the variables. The correlation coefficients between the different variables are summarized as below:
Annual sales [$000]
Area (1000 sft)
Inventory [$000]
Advertising [$000]
Households[000]
Competitors
Annual sales [$000]
1
Area (1000 sft)
0.894092082
1
Inventory [$000]
0.945503625
0.843615783
1
Advertising [$000]
0.914024068
0.748587237
0.906230642
1
Households[000]
0.953683059
0.838022883
0.863916915
0.795434449
1
Competitors
-0.912236392
-0.765737788
-0.807380423
-0.841279944
-0.869589611
1
It is observed that there are strong positive linear relationships or associations exist between the annual sales and independent variables such as area, inventory, advertising, and households. Also, it is observed that there is a strong negative linear relationship exists between the annual sales and competitors. If the number of competitors are increases, then annual sale is decreases.
Now, we have to see regression analysis for the estimation of the annual sales. For this regression model, we assume dependent variable or response variable as the annual sale and independent variables or explanatory variables as area, inventory, advertising, households, and competitors. The regression analysis is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.996583913
R Square
0.993179497
Adjusted R Square
0.991555567
Standard Error
17.64924228
Observations
27
ANOVA
df
SS
MS
F
Significance F
Regression
5
952538.941
190507.7882
611.5903232
0.00
Residual
21
6541.410811
311.4957529
Total
26
959080.3519
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-18.85940731
30.15022856
-0.625514572
0.538372488
-81.5602398
43.84142519
Area (1000 sft)
16.20157256
3.544437472
4.570985577
0.000165985
8.830511351
23.57263377
Inventory [$000]
1.746351825
0.576060683
3.031541426
0.006346786
0.548368057
2.944335593
Advertising [$000]
11.52626787
2.532103272
4.552052832
0.000173652
6.260470868
16.79206487
Households[000]
13.58031268
1.770456651
7.670514089
1.60544E-07
9.898446535
17.26217883
Competitors
-5.310971819
1.705426574
-3.114160352
0.005248871
-8.85760052
-1.764343118
The multiple correlation coefficient is given as 0.9966 which indicate strong relationship between the dependent variable and independent variables. The value of the R-square or coefficient of determination is given as 0.9932, which means about 99.32% of the variation in the dependent variable is explained by the independent variables such as area, inventory, advertising, households, and competitors.
The p-value for this regression equation is given as 0.00 which means the there is a statistically significant linear relationship exists between the dependent variable and independent variables.
Regression equation is given as below:
Annual sales = -18.85940731 + 16.20157256* Area (1000 sft) + 1.746351825*Inventory [$000] +
11.52626787*Advertising [$000] + 13.58031268* Households[000] - 5.310971819* Competitors
By using this regression equation we can easily estimate the value for annual sales.
Annual sales [$000]
Area (1000 sft)
Inventory [$000]
Advertising [$000]
Households[000]
Competitors
Annual sales [$000]
1
Area (1000 sft)
0.894092082
1
Inventory [$000]
0.945503625
0.843615783
1
Advertising [$000]
0.914024068
0.748587237
0.906230642
1
Households[000]
0.953683059
0.838022883
0.863916915
0.795434449
1
Competitors
-0.912236392
-0.765737788
-0.807380423
-0.841279944
-0.869589611
1
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